Secure and efficient routing on nodes, edges, and arcs of simple‐graphs and of multi‐graphs

Abstract

Many security companies offer patrolling services, such that guards inspect facilities or streets on a regular basis. Patrolling routes should be cost efficient, but the inspection patterns should not be predictable for offenders. We introduce this setting as a multi-objective periodic mixed capacitated general routing problem with objectives being cost minimization and route inconsistency maximization. The problem is transformed into an asymmetric capacitated vehicle routing problem, on both a simple-graph and a multi-graph; and three multi-objective frameworks using adaptive large neighborhood search are implemented to solve it. As tests with both artificial and real-world instances show that some frameworks perform better for some indicators, a hybrid search procedure, combining two of them, is developed and benchmarked against the individual solution methods. Generally, results indicate that considering more than one shortest path between nodes, can significantly increase solution quality for smaller instances, but is quickly becoming a detriment for larger instances.

Arc routing problems: A review of the past, present, and future

“…Biobjective PARPs, minimizing the total routing cost and the number of vehicles, are studied in Mei et al [159] and Zhang et al [233], whereas Fröhlich and Dörner [96] consider costs and security as the two objectives to optimize. The security of a solution is associated with route inconsistency, which measures how often links are used within given periods and whether the sequences in which the services take place have similar subsequences.…”

“…Mei et al [159] and Zhang et al [233] propose two memetic algorithms for the PCARP, Monroy et al [163] present a cluster‐first route‐second heuristic for the PCARP‐IS and in [196] an adaptive large neighborhood search is proposed for the PCARP with inventory constraints. As in other applications, transformations of the studied ARP into a node routing problem have also been proposed in Huang and Lin [123] and Fröhlich and Dörner [96].…”

“…Corberán et al [64] and Lum et al [148] incorporate different aesthetic measures to make the routes visually appealing in addition to minimizing the makespan. A nonlinear dispersion metric that tries to keep vehicles as far from each other as possible is also observed by Dhein et al [70], while Fröhlich and Dörner [96] study the route inconsistency in order to construct routes that are as different from each other as possible. All these alternative objectives have been studied only recently, and will probably receive more attention in the near future.…”

“…As for the solution methods most commonly used for multiobjective ARPs, different variants of evolutionary algorithms seem to be the most frequent ones [8,70,93,134,154,158,208,209]. Other heuristic and metaheuristic methods are proposed in [96,107,148,227]. Very few works consider the use of exact procedures [64], so this could be another future line of research.…”

Preface: Special issue on arc routing problems and other related topics

“…Fröhlich et al [5] study a multi‐objective periodic mixed capacitated general routing problem, in which nodes, edges, and arcs of the graph must be visited/traversed regularly but with inconsistent routes to ensure the unpredictability of the service patterns. The aim is to find a feasible solution that minimizes the total routing cost while maximizing the route inconsistency.…”